Yang-Baxter Equations, Computational Methods and Applications

TL;DR

This paper reviews recent advances in solving and classifying Yang-Baxter equations, introduces new set-theoretical solutions, and discusses their applications across various mathematical and computational contexts.

Contribution

It presents new set-theoretical solutions to the Yang-Baxter equation and offers unification theories and results that advance understanding of these equations.

Findings

Constructed new set-theoretical solutions

Proposed unification theories

Reviewed recent developments and applications

Abstract

Computational methods are an important tool for solving the Yang-Baxter equations(in small dimensions), for classifying (unifying) structures, and for solving related problems. This paper is an account of some of the latest developments on the Yang-Baxter equation, its set-theoretical version, and its applications. We construct new set-theoretical solutions for the Yang-Baxter equation. Unification theories and other results are proposed or proved.